Simplify the following expression: $r = \dfrac{-9n^2 - 90n - 189}{n + 3} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ r =\dfrac{-9(n^2 + 10n + 21)}{n + 3} $ Then we factor the remaining polynomial: $n^2 + {10}n + {21} $ ${3} + {7} = {10}$ ${3} \times {7} = {21}$ $ (n + {3}) (n + {7}) $ This gives us a factored expression: $\dfrac{-9(n + {3}) (n + {7})}{n + 3}$ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq -3$ Therefore $r = -9(n + 7); n \neq -3$